The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X  0 X^2+2X  X  1  1  1  1  1  1  1 2X^2  0  1  1  1  1  1 2X^2+2X  1 2X^2+X  1  1  1  1 X^2+X  1  1  1  1  X 2X^2+2X
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1  1 2X^2+2X+2  2 X+2  1  1 2X^2  1 2X^2+X X^2+1 2X^2+X+1 X^2+X 2X^2+2 2X+1 X^2+2X  1  1 2X+2 2X 2X+1 2X^2+X+1 X+1  1 X^2+2X+2  1 2X^2+1  0 2X+2 X^2+2X 2X^2+2X  0 2X^2+2X+2 X^2+X 2X+1 X^2+X  1
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 2X^2+2X+2  X 2X+1 X+1 2X+2  1 2X+1 2X^2+2X+1  1 X^2+2X+2 2X 2X+1 2X^2+2X  2 X^2+X X^2+2 2X^2+2X+2 X^2+2X+2 2X^2+2 2X^2+1 2X^2  1 X^2+X+2 X^2+X 2X^2+2 2X+1 X^2+2X  0  1 X^2+2  X X^2+1 2X^2+2X+2  1 2X^2
 0  0  0 2X 2X^2 X^2  0 X^2+2X 2X^2+X  X 2X^2  0 X^2+2X 2X^2+X X^2+2X  X X^2 2X 2X^2+2X 2X^2+2X 2X^2+X X^2+X 2X^2+2X X^2+X X^2 2X^2+2X 2X  X X^2+2X X^2+X 2X^2+X 2X^2 2X^2+X  X 2X  X  0 X^2+2X 2X^2  0  0 2X  X

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+702x^77+1194x^78+2304x^79+4818x^80+5884x^81+8748x^82+13440x^83+15282x^84+19008x^85+25356x^86+21120x^87+21402x^88+17916x^89+10082x^90+5292x^91+3012x^92+1008x^93+108x^94+240x^95+78x^96+108x^98+26x^99+18x^101

The gray image is a linear code over GF(3) with n=387, k=11 and d=231.
This code was found by Heurico 1.16 in 41.7 seconds.